I had heard of Now (https://zeit.co) but hadn't tried it until today. It's nifty. So nifty that I'm using it to publish this site (notes.baty.net). I simply type "now" while in the directory these static files are in and it just happens. SSL included.

The thing that wasn't immediately obvious was that each time you deploy, a new URL is used. This means that the alias needs to be updated each time. Seemed inconvenient, and some digging revealed that putting the default alias in a now.json file does the trick.